Geodesic
A new perspective on the average mixing matrix
Gabriel Coutinho1 ; Chris Godsil2 ; Krystal Guo3 ; Hanmeng Zhan2
1Universidade Federal de Minas Gerais
2University of Waterloo
3Université libre de Bruxelles
The electronic journal of combinatorics, Tome 25 (2018) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about the quantum walk and about the graph. We show that it is the matrix of transformation of the orthogonal projection onto the commutant algebra of the adjacency matrix, restricted to diagonal matrices. Using this formulation of the average mixing matrix, we find connections between its rank and automorphisms of the graph.
DOI : 10.37236/7867
Classification : 05C50, 05C81
Mots-clés : algebraic graph theory, quantum walks, average mixing matrix

Gabriel Coutinho  1   ; Chris Godsil  2   ; Krystal Guo  3   ; Hanmeng Zhan  2

1 Universidade Federal de Minas Gerais
2 University of Waterloo
3 Université libre de Bruxelles 
@article{10_37236_7867,
     author = {Gabriel Coutinho and Chris Godsil and Krystal Guo and Hanmeng Zhan},
     title = {A new perspective on the average mixing matrix},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {4},
     doi = {10.37236/7867},
     zbl = {1401.05182},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7867/}
}
TY  - JOUR
AU  - Gabriel Coutinho
AU  - Chris Godsil
AU  - Krystal Guo
AU  - Hanmeng Zhan
TI  - A new perspective on the average mixing matrix
JO  - The electronic journal of combinatorics
PY  - 2018
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/7867/
DO  - 10.37236/7867
ID  - 10_37236_7867
ER  - 
%0 Journal Article
%A Gabriel Coutinho
%A Chris Godsil
%A Krystal Guo
%A Hanmeng Zhan
%T A new perspective on the average mixing matrix
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7867/
%R 10.37236/7867
%F 10_37236_7867
Gabriel Coutinho; Chris Godsil; Krystal Guo; Hanmeng Zhan. A new perspective on the average mixing matrix. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7867

Cité par Sources :